Start by cutting the potato into chunks, peel and cut the chayote into chunks and cut the green beans into 1" pieces.
Put the potatoes in a pot, cover with water. Bring the water to a boil and cook for 10 minutes.
Add the Chayote and cook for 5 more minutes.
Add the green beans and cook for another 3 minutes or so.
Drain and reserve the vegetables. If you are making a vegetarian version of this recipe, reserve the cooking water.
Combine 1 1/2 Cups Masa Harina with 1 1/2 Cups warm water.
Mix until it can form a ball and separate it into halves.
Make Chochoyotes: Use one half of the masa dough. Add 1 tsp Salt and 1 Tbls Oil and mix well. Take 1 tsp of dough, roll it into a ball and make an indentation with your thumb. Repeat until all the dough is used up. Set aside.
Put the other half of the dough into a blender along with 3/4 Cup of Chicken Stock. (Vegetable Stock if you are making this vegetarian). Blend until very smooth. Reserve.
Prepare the Chicken: Cut the chicken into bite size chunks. Heat a Tbls of oil in a skillet and add the chicken. Cook the first side for three minutes and then turn the pieces over and cook the other side about two minutes. The chicken will cook a bit more in the molé so it doesn't need to be all the way cooked at this point. Set aside.
Remove the seeds and stems from the chiles and tear them into small pieces. Put them in a saucepan.
With a sharp knife, lightly score the top and bottom of the tomatoes with an 'X'. Add the tomatillos and tomatoes and 1 to 1 1/2 cups of chicken broth to the saucepan with the chiles.
Bring this to a boil and cook, covered, for 8 to 10 minutes. The tomatillos will turn bright green and the tomato skins will start to detach. Take the tomatoes out to cool a bit before taking the peels off of them.
Add the tomatoes and the other contents of the saucepan to a blender.
Add 1/4 of an onion, chopped, 5 garlic cloves, cinnamon, cumin, Mexican oregano, cloves and black pepper. Add another half cup of chicken stock and blend thoroughly. At this point you have the option to push the sauce through a fine mesh strainer to make it really smooth.
Put 2 tablespoons oil in a large stock pot. When the oil is hot add the contents of the blender. This will spatter as it heats up so be sure to cover it. Add the remaining chicken stock to the blender, give it a quick blitz and add it to the pot. That will get any remaining sauce out of the blender. Cook for 10 minutes stirring frequently.
Add the masa/broth slurry that you made in step 9 to the pot and keep stirring as it thickens. Cook for another 10 minutes and you will really see the sauce thickening.
Add the chicken and cook for 2 minutes and then add the vegetables. Cook this all together for about 10 minutes to get all the flavors married. The molé should be getting quite thick so continue stirring to keep it from sticking to the bottom.
Add the chochoyotes. fold these into the stew gently so they don't just break up. Cook this for another 5 to 10 minutes and the molé is ready to serve.
Ladle into bowls and garnish with lime wedges.